Portability | to be determined |
---|---|

Stability | experimental |

Maintainer | stephen.tetley@gmail.com |

Plainly named combinators

Sometimes permuted to be generally useful...

Note the fixity of `(#)`

and `(##)`

is not yet *fixed*.
Some experience needs to be gathered as to whether the
precendence levels are appropriate.

- (#) :: a -> (a -> b) -> b
- (##) :: (a -> b) -> (b -> c) -> a -> c
- subst :: (a -> b -> c) -> (a -> b) -> a -> c
- bigphi :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d
- appro :: (c -> d -> e) -> (a -> c) -> (b -> d) -> a -> b -> e
- dup :: (a -> a -> b) -> a -> b
- oo :: (c -> d) -> (a -> b -> c) -> a -> b -> d
- ooo :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
- oooo :: (e -> f) -> (a -> b -> c -> d -> e) -> a -> b -> c -> d -> f
- combfi :: (c -> b -> d) -> (a -> c) -> a -> b -> d
- combfii :: (d -> b -> c -> e) -> (a -> d) -> a -> b -> c -> e
- combfiii :: (e -> b -> c -> d -> f) -> (a -> e) -> a -> b -> c -> d -> f

# The real stuff

(#) :: a -> (a -> b) -> bSource

T combinator - thrush

Reverse application - the T combinator. Found in Peter Thiemann's WASH and the paper 'Client-Side Web Scripting in Haskell' - Erik Meijer, Daan Leijen & James Hook.

(##) :: (a -> b) -> (b -> c) -> a -> cSource

Q Combinator - the queer bitd.

Reverse composition - found in Peter Thiemann's WASH. You might perfer to use (<<<) from Control.Categoty.

subst :: (a -> b -> c) -> (a -> b) -> a -> cSource

S combinator - subst.
Familiar as Applicative's (`<*>`

) operator, which itself is
fmap:

f (b -> c) -> f b -> f c where f = ((->) a)

bigphi :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> dSource

The big Phi, or Turner's `S'`

combinator.
Known to Haskell programmers as liftA2 and liftM2 for the
Applicative and Monad instances of (->).

(a1 -> a2 -> r) -> m a1 -> m a2 -> m r where m = ((->) a)

Taste suggests you may prefer liftA2 especially as `bigphi`

is
not a great name (calling it s' would take a very useful
variable name).

appro :: (c -> d -> e) -> (a -> c) -> (b -> d) -> a -> b -> eSource

A variant of the `D2`

or dovekie combinator - the argument
order has been changed to be more satisfying for Haskellers:

(appro comb f g) x y

(f x) `comb` (g y)

`on`

from Data.Function is similar but less general, where
the two intermediate results are formed by applying the same
function to the supplied arguments:

on = (appro comb f f)

dup :: (a -> a -> b) -> a -> bSource

dup - duplicator aka the W combinator aka Warbler.

dup f x = f x x

# Specs

oo :: (c -> d) -> (a -> b -> c) -> a -> b -> dSource

Compose an arity 1 function with an arity 2 function. B1 - blackbird

ooo :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> eSource

Compose an arity 1 function with an arity 3 function. B2 - bunting

oooo :: (e -> f) -> (a -> b -> c -> d -> e) -> a -> b -> c -> d -> fSource

Compose an arity 1 function with an arity 4 function.

# Combiners

combfi :: (c -> b -> d) -> (a -> c) -> a -> b -> dSource

Combiners - similar to the cardinal' combinator.

Mnemonically - `comb`

(ine) after applying `f`

to `x`

and a
single identity: `y`

.

combfi comb f x y = comb (f x) y

Equivalently:

combfi comb f = appro comb f id

But combfi is a useful introduction to the (somewhat manic, but sometimes useful) higher arity versions.